The projector-augmented wave (PAW) method is one of the approaches that are widely used to approximately treat core electrons and thus to speed up plane-wave basis set electronic structure calculations. However, PAW involves approximations, and it is thus important to understand how they affect the results. Tests of the precision of PAW data sets often use the properties of isolated atoms or atomic solids. While this is sufficient to identify problematic PAW data sets, little information has been gained to understand the origins of the errors and suggest ways to correct them. Here, we show that the interaction energies of molecular dimers are very useful not only to identify problematic PAW data sets but also to uncover the origin of the errors. Using dimers from the S22 and S66 test sets and other dimers, we find that the error in the interaction energy is composed of a short-range component with an exponential decay and a long-range electrostatic part caused by an error in the total charge density. We propose and evaluate a simple improvable scheme to correct the long-range error and find that even in its simple and readily usable form, it is able to reduce the interaction energy errors to less than half on average for hydrogen-bonded dimers.

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Recent discovery of an unusual bond between Na and B in NaBH3- motivated us to look for potentially similar bonds, which remained unnoticed among systems isoelectronic with NaBH3-. Here, we report a novel family of collective interactions and a measure called exchange-correlation interaction collectivity index (ICIXC; [Formula: see text]) to characterize the extent of collective versus pairwise bonding. Unlike conventional bonds in which ICIXC remains close to one, in collective interactions ICIXC may approach zero. We show that collective interactions are commonplace among widely used organometallics, as well as among boron and aluminum complexes with the general formula [Ma+AR3]b- (A: C, B or Al). In these species, the metal atom interacts more efficiently with the substituents (R) on the central atoms than the central atoms (A) upon forming efficient collective interactions. Furthermore, collective interactions were also found among fluorine atoms of XFn systems (X: B or C). Some of organolithium and organomagnesium species have the lowest ICIXC among the more than 100 studied systems revealing the fact that collective interactions are rather a rule than an exception among organometallic species.

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